Distinguishing the cause and effect from bivariate observational data is the
foundational problem that finds applications in many scientific disciplines.
One solution to this problem is assuming that cause and effect are generated
from a structural causal model, enabling identification of the causal direction
after estimating the model in each direction. The heteroscedastic noise model
is a type of structural causal model where the cause can contribute to both the
mean and variance of the noise. Current methods for estimating heteroscedastic
noise models choose the Gaussian likelihood as the optimization objective which
can be suboptimal and unstable when the data has a non-Gaussian distribution.
To address this limitation, we propose a novel approach to estimating this
model with Student's $t$-distribution, which is known for its robustness in
accounting for sampling variability with smaller sample sizes and extreme
values without significantly altering the overall distribution shape. This
adaptability is beneficial for capturing the parameters of the noise
distribution in heteroscedastic noise models. Our empirical evaluations
demonstrate that our estimators are more robust and achieve better overall
performance across synthetic and real benchmarks.

通过使用学生 t 分布提出了一种估计异方差噪声模型的新方法，以解决现有估计方法在数据分布非高斯时存在的亚优和不稳定问题，并成功地在合成和真实基准测试中表现出更好的鲁棒性和整体性能。

鲁棒估计因果异方差噪声模型

Robust Estimation of Causal Heteroscedastic Noise Models

We study the class of location-scale or heteroscedastic noise models (LSNMs),
in which the effect $Y$ can be written as a function of the cause $X$ and a
noise source $N$ independent of $X$, which may be scaled by a positive function
$g$ over the cause, i.e., $Y = f(X) + g(X)N$. Despite the generality of the
model class, we show the causal direction is identifiable up to some
pathological cases. To empirically validate these theoretical findings, we
propose two estimators for LSNMs: an estimator based on (non-linear) feature
maps, and one based on probabilistic neural networks. Both model the
conditional distribution of $Y$ given $X$ as a Gaussian parameterized by its
natural parameters. Since the neural network approach can fit functions of
arbitrary complexity, it has an edge over the feature map-based approach in
terms of empirical performance. When the feature maps are correctly specified,
however, we can prove that our estimator is jointly concave, which allows us to
derive stronger guarantees for the cause-effect identification task.

研究了一类称为 location-scale 或 heteroscedastic 噪声模型（LSNM）的模型，提出了两种估计器，并通过 probabilistic 神经网络计算了条件分布的函数，从而证明了在某些病理情况下，因果关系可确定。